ANALYTICAL AND NUMERICAL SIMULATION OF TEMPERATURE RELIANT THERMAL CONDUCTIVITY AND VISCOSITY DISPARITY EFFECTS ON THE ONSET OF CELLULAR CONVECTIVE MOTION IN A VISCOELASTIC OLDROYD-B FLUID SATURATED PERMEABLE LAYER

In this work, we inspected, analytically and numerically, the influences of temperature reliant thermal conductivity and viscosity disparities on the onset of cellular convective wave in an Oldroyd-B viscoelastic water-saturated permeable layer. The problem is applicable to cellular foams designed from plastics, ceramics, and metallic sources where radiative conductivity is demonstrated as an exponent function of temperature. The approximate analytical criteria for the marginal and overstable types of convective waves are determined using a one-term Galerkin method. The numerical outcomes accurate to one decimal place are also provided using a higher-order Galerkin method. The investigation demonstrates that the overstable convective motion arises only when the estimate of the stress relaxation factor is greater than the strain retardation factor. The effect of the thermal conductivity inconsistency factor, strain retardation factor, and heat capacity ratio is to postpone the convective wave, whereas the viscosity inconsistency factor and the stress relaxation factor promote it. The range of the convective cell degenerates with accumulating thermal conductivity inconsistency factor and heat capacity ratio, whereas it increases with the strain retardation factor. The frequency of oscillations of overstable convection increases with the thermal conductivity inconsistency factor and the stress relaxation factor, whereas it declines with the strain retardation factor and heat capacity ratio. The current results are in line with the available literature related to the specific case of this research.